Introduction to Cryptography with Mathematical Foundations and Computer Implementations

by Alexander Stanoyevitch

From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed. Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with "Exercises for the Reader;" complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms. As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography.

672 pages, Hardcover

First published August 11, 2010

Reviews

[Sumeya Yeniza]

good

[Sheffielder · Rating 3 out of 5]

The book appears to be extremely readable, and judging by the speed with which I'm getting through it, ought to be eminently suitable as a text book. Moreover, the book appears to explain from scratch all of the discrete mathematics that is used, and provides a large number of worked exercises. Of course, this potentially reduces its suitability for advanced computer science undergraduates, who would hopefully already be familiar with the formal underpinnings.

There are a couple of negative points, however. Most significant is the way the publisher (presumably) has decided to include extremely wide margins on the pages - in many places, less than half the available white space is actually used for print. This is a gross waste of paper, and presumably ramps up the book's price completely unnecessarily.

There is also at least one technical error in the footnotes. We are told on page 4 that "it is always possible to represent any element of a discrete set with a finite string (in some alphabet)", where an "alphabet" has previously been defined to mean "any finite set of symbols". This is obviously only true for countable discrete sets; uncountable discrete sets cannot be represented in this way, because there are only countably many finite strings over a finite alphabet.

Nonetheless, this book gives a good account of the field, with due emphasis on key mathematical concepts underpinning it.